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IMA Journal of Applied Mathematics 2003 68(6):621-635; doi:10.1093/imamat/68.6.621
© 2003 by Institute of Mathematics and its Applications
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On the domain derivative for scattering by impenetrable obstacles in chiral media

Roland Potthast1 and Ioannis G. Stratis2

1 Institute of Numerical and Applied Mathematics, University of Göttingen, Lotzestrasse 16-18, D-37083 Göttingen, Germany 2 Department of Mathematics, University of Athens, Panepistimiopolis, GR-15784 Zographou, Athens, Greece

For scattering of electromagnetic waves in a chiral medium by some perfectly conducting inclusions, we study the dependence of the scattered field on the boundary of the inclusions and show its Fréchet differentiability in appropriate spaces. Further, we derive a characterization of the derivative as a solution to some corresponding chiral boundary value problem. Our proof contains a new approach to rigorously derive this characterization.

Keywords: chiral media; domain derivative; Fréchet differentiability.

Received 5 June 2002. Revised 9 December 2002.


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